Finite Group Databasebeta

← #10800982

Subgroups — #10800982

Order 768.

1344 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5812C211yesmaximal, characteristic
2C2×C3×#451C211yesmaximal, characteristic
3C2×#5184C211yesmaximal, characteristic, complemented
4C2×Dic3×Q16C211yesmaximal, characteristic, complemented
5#82744C211yesmaximal, characteristic
6#72132C211yesmaximal, characteristic
7#72065C211yesmaximal, characteristic, complemented
8#72065C211yesmaximal, characteristic, complemented
9#71693C211yesmaximal, characteristic
10#70238C211yesmaximal, characteristic, complemented
11#70236C211yesmaximal, characteristic, complemented
12#70220C211yesmaximal, characteristic, complemented
13Dic3×#103C211yesmaximal, characteristic, complemented
14#69929C211yesmaximal, characteristic
15#69907C211yesmaximal, characteristic
16#21463—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21#5812—24no—
22#5812—24no—
23C2×Q8×Dic3—21no—
24C2×Q8×Dic3—21no—
25C2×Q8×Dic3C2211yescharacteristic
26C2×Q8×Dic3C2211yescharacteristic
27C2×Q8×Dic3C2211yescharacteristic
28C2×Q8×Dic3C2211yescharacteristic
29C2×Q8×Dic3C2211yescharacteristic
30C2×#926—21no—
31C2×#926—21no—
32C2×#926C2211yescharacteristic
33C2×#926C2211yescharacteristic
34C3×#451C418yescomplemented
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38#5229C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#835C2211yescharacteristic
45#5212C2211yescharacteristic
46C2×#830C2211yescharacteristic
47#5184—24no—
48Dic3×Q16—24no—
49C2×#818C2211yescharacteristic
50C2×#817C2211yescharacteristic
51C2×#815C2211yescharacteristic
52C2×C8×Dic3C2211yescharacteristic
53#4984—21no—
54#4984C2211yescharacteristic
55#4980—21no—
56Dic3×C4⋊C4C2211yescharacteristic
57#4951—21no—
58#4951—21no—
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#519—31no—
66C2×#451D311yescharacteristic
67C2×#441—31no—
68C2×C4×Q16—31no—
69#2323—31no—
70#1878—31no—
71#1878—31no—
72#1873—31no—
73#1865—31no—
74#1863—31no—
75#1854—31no—
76#1787—31no—
77#1763—31no—
78C4×#103—31no—
79#1750—31no—
80C22×C3×Q8—22no—
81C22×C3×Q8—22no—
82C22×C3×Q8—22no—
83C22×C3×Q8—22no—
84C22×C3×Q8—21no—
85C22×C3×Q8—22no—
86C22×C3×Q8C2×C414yes—
87C22×C3×Q8C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×Q8C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C2×C3×Q16—22no—
93C2×C3×Q16—22no—
94C2×C3×Q16—22no—
95C2×C3×Q16—22no—
96C2×C3×Q16C2×C414yes—
97C2×C3×Q16C2×C414yes—
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8C2×C414yes—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217D411yescharacteristic
108C2×#217D411yescharacteristic
109Q8×Dic3—28no—
110Q8×Dic3—28no—
111Q8×Dic3—22no—
112Q8×Dic3—22no—
113Q8×Dic3—22no—
114Q8×Dic3—22no—
115Q8×Dic3—22no—
116Q8×Dic3—22no—
117Q8×Dic3—22no—
118Q8×Dic3—22no—
119Q8×Dic3D414yes—
120Q8×Dic3D414yes—
121#926—28no—
122#926—28no—
123#926—22no—
124#926—22no—
125#926—22no—
126#926—22no—
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3D411yescharacteristic
134C2×C4⋊Dic3D411yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4×Dic3—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3—21no—
142C2×C4×Dic3—21no—
143C2×C4×Dic3—21no—
144C2×C4×Dic3—21no—
145C2×C4×Dic3—21no—
146C2×C4×Dic3C2311yescharacteristic
147C2×C4×Dic3C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150C3×#103C2×C414yes—
151C3×#103C2×C414yes—
152C3×C22⋊C8C2×C414yes—
153#835—22no—
154#835—22no—
155#835—22no—
156#835—22no—
157#835—22no—
158#835—22no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164#830—22no—
165#818—22no—
166#817—22no—
167#815—22no—
168C8×Dic3—22no—
169C23×Q8C2×D311yescharacteristic
170C22×Q16C2×D311yescharacteristic
171C22×Q16C2×D311yescharacteristic
172C2×C22⋊Q8C2×D311yescharacteristic
173#519—64no—
174#519—64no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×Q8—31no—
178C2×C4×Q8—31no—
179C2×C4×Q8—31no—
180C2×C4×Q8—61no—
181C2×C4×Q8—61no—
182C2×#117—31no—
183C2×#117—31no—
184C2×#117—61no—
185C2×#117—61no—
186#451Dic318yescomplemented
187#441—64no—
188C4×Q16—64no—
189C2×#107—31no—
190C2×#106—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103C2×D311yescharacteristic
198C2×#103C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8C2×D311yescharacteristic
201C2×#97—31no—
202C2×C4×C8—31no—
203#391—31no—
204#389—31no—
205#389—61no—
206#388—61no—
207#388—61no—
208#387—61no—
209#380—31no—
210C4×C4⋊C4—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C2×C3×Q8—24no—
219C2×C3×Q8—28no—
220C2×C3×Q8—28no—
221C2×C3×Q8—24no—
222C2×C3×Q8—28no—
223C2×C3×Q8—28no—
224C2×C3×Q8—24no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8C22×C412yes—
237C2×C3×Q8C22×C412yes—
238C2×C3×Q8C22×C412yes—
239C2×C3×Q8C2×D412yes—
240C2×C3×Q8C2×D412yes—
241C2×C3×Q8#4112yes—
242C2×C3×Q8#4112yes—
243C22×C3×C4—24no—
244C22×C3×C4—24no—
245C22×C3×C4—24no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4C22×C412yes—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4#4112yes—
257C22×C3×C4C2411yescharacteristic
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C22×Dic3C2×D411yescharacteristic
266C3×Q16—28no—
267C3×Q16—28no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8C22×C412yes—
273C2×C3×C8C22×C412yes—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4C22×C412yes—
277C3×C22⋊C4—24no—
278#217—24no—
279#217—22no—
280#217—22no—
281#217—81no—
282C4⋊Dic3—24no—
283C4⋊Dic3—24no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—24no—
287C4⋊Dic3—24no—
288C4⋊Dic3—22no—
289C4⋊Dic3—22no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—42no—
295C4⋊Dic3—81no—
296C4⋊Dic3C2×D412yes—
297C4⋊Dic3C2×D412yes—
298C4×Dic3—24no—
299C4×Dic3—24no—
300C4×Dic3—24no—
301C4×Dic3—21no—
302C4×Dic3—21no—
303C4×Dic3—24no—
304C4×Dic3—24no—
305C4×Dic3—42no—
306C4×Dic3—81no—
307C4×Dic3C2×D412yes—
308C4×Dic3C2×D412yes—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—21no—
320C22×Q8—22no—
321C22×Q8C2×Dic314yes—
322C22×Q8C22×D311yescharacteristic
323C22×Q8C22×D311yescharacteristic
324C22×Q8C22×D311yescharacteristic
325C23×C4—21no—
326C23×C4C22×D311yescharacteristic
327C2×Q16—22no—
328C2×Q16—22no—
329C2×Q16—22no—
330C2×Q16—22no—
331C2×Q16C2×Dic314yes—
332C2×Q16C2×Dic314yes—
333C22×C8—31no—
334C22×C8—31no—
335C22×C8C22×D311yescharacteristic
336C22×C8C22×D311yescharacteristic
337C22⋊Q8—22no—
338C22⋊Q8C2×Dic314yes—
339C4×Q8—34no—
340C4×Q8—34no—
341C4×Q8—62no—
342C4×Q8—62no—
343C4×Q8—62no—
344C4×Q8—62no—
345C4×Q8—62no—
346C4×Q8—62no—
347C4×Q8—68no—
348C4×Q8—68no—
349C4×Q8—62no—
350C4×Q8—62no—
351#117—62no—
352#117—62no—
353#117—62no—
354#117—62no—
355#117—68no—
356#117—68no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—31no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C42—31no—
377C2×C42—31no—
378C2×C42—61no—
379C2×C42—61no—
380C2×C42—61no—
381C2×C42—61no—
382C2×C42—61no—
383C2×C42—61no—
384C2×C42—61no—
385#107—62no—
386#106—62no—
387#103—62no—
388#103—62no—
389#103—62no—
390#103—62no—
391#103—62no—
392#103—62no—
393#103C2×Dic314yes—
394#103C2×Dic314yes—
395C22⋊C8—62no—
396C22⋊C8C2×Dic314yes—
397#97—62no—
398C4×C8—62no—
399#95—61no—
400#95—61no—
401#95—61no—
402#95—61no—
403#95—61no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3C4×D412yes—
411C23×C3C22×D411yescharacteristic
412C3×Q8—216no—
413C3×Q8—22no—
414C3×Q8—22no—
415C3×Q8—22no—
416C3×Q8—22no—
417C3×Q8—22no—
418C3×Q8—22no—
419C3×Q8—22no—
420C3×Q8—22no—
421C3×Q8—41no—
422C3×Q8—41no—
423C3×Q8C4×D414yes—
424C3×Q8C4×D414yes—
425C2×C3×C4—216no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4C4×D412yes—
445C2×C3×C4C23×C411yescharacteristic
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3#12012yes—
474C2×Dic3#12012yes—
475C3×C8—22no—
476C3×C8—22no—
477C3⋊C8—41no—
478C3⋊C8—41no—
479C24D3×D411yescharacteristic
480C2×Q8—24no—
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—24no—
484C2×Q8—28no—
485C2×Q8—28no—
486C2×Q8—24no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8D3×D412yes—
499C2×Q8D3×D412yes—
500C2×Q8#23712yes—
501C2×Q8#23712yes—
502C2×Q8C22×Dic312yes—
503C2×Q8C22×Dic312yes—
504C2×Q8C22×Dic312yes—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—31no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4D3×D411yescharacteristic
525C22×C4#23712yes—
526C22×C4C22×Dic312yes—
527C22×C4C23×D311yescharacteristic
528Q16—28no—
529Q16—28no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8C22×Dic312yes—
541C2×C8C22×Dic312yes—
542C4⋊C4—24no—
543C4⋊C4—21no—
544C4⋊C4—32no—
545C4⋊C4—32no—
546C4⋊C4—62no—
547C4⋊C4—62no—
548C4⋊C4—64no—
549C4⋊C4—64no—
550C4⋊C4—64no—
551C4⋊C4—64no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—122no—
559C4⋊C4—241no—
560C4⋊C4C22×Dic312yes—
561C22⋊C4—24no—
562C22⋊C4—62no—
563C22⋊C4—62no—
564C22⋊C4—64no—
565C22⋊C4—241no—
566C42—32no—
567C42—32no—
568C42—64no—
569C42—64no—
570C42—64no—
571C42—64no—
572C42—64no—
573C42—61no—
574C42—61no—
575C42—122no—
576C42—241no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3C2×C4×D411yescharacteristic
585C22×C3C2×#12011yescharacteristic
586C22×C3#52511yescharacteristic
587C22×C3#57711yescharacteristic
588C22×C3#57811yescharacteristic
589C22×C3#57811yescharacteristic
590C22×C3#57811yescharacteristic
591C3×C4—24no—
592C3×C4—24no—
593C3×C4—22no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4C2×C4×D411yescharacteristic
597C3×C4C2×C4×D411yescharacteristic
598C3×C4#52511yescharacteristic
599C3×C4#52511yescharacteristic
600Dic3—22no—
601Dic3—22no—
602Dic3—41no—
603Dic3—42no—
604Dic3—41no—
605Dic3—42no—
606Dic3—81no—
607Dic3—81no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23D4×Dic312yes—
615C23C2×D3×D411yescharacteristic
616Q8—216no—
617Q8—22no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—22no—
623Q8—22no—
624Q8—22no—
625Q8—41no—
626Q8—41no—
627Q8D4×Dic314yes—
628Q8D4×Dic314yes—
629C2×C4—216no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—32no—
645C2×C4—32no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4D4×Dic312yes—
673C2×C4C2×D3×D411yescharacteristic
674C2×C4C2×D3×D411yescharacteristic
675C2×C4C2×#23711yescharacteristic
676C2×C4C2×#23711yescharacteristic
677C2×C4C2×#23711yescharacteristic
678C2×C4C23×Dic311yescharacteristic
679C8—22no—
680C8—22no—
681C8—121no—
682C8—121no—
683C2×C3—42no—
684C2×C3C4×#12011yescharacteristic
685C2×C3#294711yescharacteristic
686C2×C3#295011yescharacteristic
687C2×C3#301111yescharacteristic
688C2×C3#301311yescharacteristic
689C2×C3#312111yescharacteristic
690C2×C3#312711yescharacteristic
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22#558611yescharacteristic
699C22D3×#12011yescharacteristic
700C22#576611yescharacteristic
701C22#576611yescharacteristic
702C22#577811yescharacteristic
703C22#577911yescharacteristic
704C22C2×D4×Dic311yescharacteristic
705C4—24no—
706C4—24no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—62no—
711C4—62no—
712C4—121no—
713C4—122no—
714C4—121no—
715C4—122no—
716C4—241no—
717C4—241no—
718C4#558611yescharacteristic
719C4#558611yescharacteristic
720C4C2×D4×Dic311yescharacteristic
721C4C2×D4×Dic311yescharacteristic
722C3#2146311yescharacteristic, complemented, Sylow
723C2—42no—
724C2#8017611yescharacteristic
725C2#8017711yescharacteristic
726C2#8018511yescharacteristic
727C2#8018611yescharacteristic
728C2Dic3×#12011yescharacteristic
729C2#8387411yescharacteristic
730C2#8396511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#451C2
socleC23×C3C22×D4
prime radicalC24×C3C2×D4
cosocleC22×C3×C4C24
hypercenterC2×#451D3
hypocenterC3#21463
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#5184C2semidirect
4. C2×Dic3×Q16C2semidirect
7. #72065C2semidirect
8. #72065C2semidirect
10. #70238C2semidirect
11. #70236C2semidirect
12. #70220C2semidirect
13. Dic3×#103C2semidirect
34. C3×#451C4semidirect
186. #451Dic3semidirect
722. C3#21463semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#58122
C2×C3×#4512
C2×#51842
C2×Dic3×Q162
#827442
#721322
#720652
#716932
#702382
#702362
#702202
Dic3×#1032
#699292
#699072
#214633